Abstract: The inherent multi-physics and multi-scale features of many real world problems accentuate the importance to develop efficient and stable numerical methods for the relevant PDEs, especially the decoupling methods. Although great efforts have been made for solving these problems, many practical and analytical challenges remain to be solved. This mini-symposium intends to create a forum for junior and senior researchers from different fields to discuss recent advances on the decoupling methods for multi-physics and multi-scale problems with their applications.

MS-We-D-27-113:30--14:00Time-Parallel Methods Based on Waveform Relaxation for Time-dependent Differential EquationsSong, Bo (Xi'an Jiaotong Univ.)Jiang, Yao-Lin (Xi'an Jiaotong Univ./Xinjiang Univ.)Abstract: The parareal algorithm, which permits to solve evolution problems in a time parallel fashion, has created a lot of attention over the past decade. In this talk, we will present a parareal algorithm with the waveform relaxation propagator as the fine propagator for initial-value and time-periodic differential equations. Especially, we will present two new parareal algorithms for time-periodic problems. Several realistic applications are also provided to illustrate the effectiveness of the new strategies.

MS-We-D-27-214:00--14:30A simple treatment of the corner singularity using nonconforming elements for cavity flowSheen, Dongwoo (Seoul National Univ.)Abstract: In the numerical simulation of cavity flow, one needs to pay attention to deal with
the well-known corner singularities. In particular, if conforming finite
elements are used, special care should be taken of.
In this talk we will introduce a simple treatment of
corner singularity using stable cheapest nonconforming elements for cavity
flow.
Several numerical comparisons show superiority with the proposed method.

MS-We-D-27-314:30--15:00Solving an inverse Stefan problem by a novel fictitious domain method Huang, Jianguo (Shanghai Jiao Tong Univ.)Abstract: A novel fictitious domain method is proposed for solving an inverse Stefan problem, in order to determine a free boundary during the phase transition, by means of measurement data of temperature and heat flux at the left end point of the material. Theoretical analysis and numerical simulation are provided to show the computational performance of the method. This is a joint work with Huashan Sheng and Wan Tang from Shanghai Jiao Tong University.